quantum field theory

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1、QUANTUMFIELDTHEORYNotestakenfromacourseofR.E.Borcherds,Fall2001,BerkeleyRichardE.Borcherds,Mathematicsdepartment,EvansHall,UCBerkeley,CA94720,U.S.A.e{mail:reb@math.berkeley.eduhomepage:www.math.berkeley.edu/~rebAlexBarnard,Mathematicsdepartment,EvansHall,UCBer

2、keley,CA94720,U.S.A.e{mail:barnard@math.berkeley.eduhomepage:www.math.berkeley.edu/~barnardContents1Introduction21.1LifeCycleofaTheoreticalPhysicist.......................21.2HistoricalSurveyoftheStandardModel.....................31.3SomeProblemswithNeutrinos.

3、.........................71.4ElementaryParticlesintheStandardModel...................82Lagrangians92.1WhatisaLagrangian?...............................9arXiv:math-ph/0204014v18Apr20022.2Examples......................................92.3TheGeneralEuler{Lagrange

4、Equation......................113SymmetriesandCurrents123.1ObviousSymmetries................................123.2Not{So{ObviousSymmetries...........................143.3TheElectromagneticField.............................1513.4ConvertingClassicalFieldTheorytoH

5、omologicalAlgebra...........174FeynmanPathIntegrals194.1FiniteDimensionalIntegrals............................194.2TheFreeFieldCase................................204.3FreeFieldGreen'sFunctions...........................214.4TheNon-FreeCase....................

6、.............2250-DimensionalQFT235.1BorelSummation..................................265.2OtherGraphSums.................................265.3TheClassicalField.................................275.4TheEectiveAction................................296Distribution

7、sandPropagators336.1EuclideanPropagators...............................346.2LorentzianPropagators..............................366.3WavefrontsandDistributionProducts......................387HigherDimensionalQFT427.1AnExample....................................

8、.427.2RenormalisationPrescriptions...........................437.3FiniteRenormalisations..............................457.4AGroupStructureonFiniteRenormalisations.................4